How do you do this question?

V=864π/5

The 2nd shaded picture matches our volume. And the 1st 3D picture maps the volume once rotated.

Step-by-step explanation:

The idea is that you're revolving the graph around an axis and getting a would-be solid objective. Think of it as finding the volume of a cylinder but instead of straight edges going up the height, the height follows a portion of a graph. We take the area of the circle with a variable radius and plug it into the integral:

∫πr²dy/dx

You need to know what axis you're revolving around, determine the radius of the shape, then your height which will determine variable you're integrating with respect to.

So with that we plug in the r and simplify as needed before integrating to get the answer.

My work is in the attachment. Comment with any questions.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

it would open into a square depending on the type of envelope i’m not sure about the second part